You as the employer are risk neutral. You seek to maximize your net profit from these two workers.
(a) Suppose that you could at zero cost monitor the efforts of the two workers. Would you want to make them work hard, or is it better to have them loaf? What payments would you offer them?
(b) Suppose that you cannot monitor the efforts of the two workers. You can, however, sign a contract of the form: I agree to pay $X if the task you perform has value $10 to me, and $Y if the task has value $0. Subject to the constraints that the worker must be willing to sign, and the worker, seeing what is being paid, will choose how hard to work, what is the best contract of this form for you? (The worker will resolve all ties in his utility in your favor.)
Now suppose that you cannot monitor the two, but you can offer them more complex contracts, of the following form: I agree to pay $X if both of you produce a $10 outcome for me, $Y if you produce a $10 outcome and your fellow worker produces $0, $Z if you produce $0 and your fellow worker produces a $10 outcome, and $W if you both produce $0.
(c) What contracts of this form are optimal if you want to induce both workers to loaf?
(d) Suppose that you wish to offer contracts that will induce both to work hard. Imagine that this means you must meet the following constraints: Each worker must be induced to take the contract; each worker, assuming that his fellow worker is going to work hard, must be induced to work hard. What is the optimal contract to offer in this case?
(e) You are worried that the contract offered in (d) might induce the follow ing behavior: Each worker will loaf. You would feel less worried about this possibility if you knew that each one, given the other was loafing, would prefer to work hard. If you add this constraint to part (d), is the old solution still valid? If not, what is the new solution?·
(f) Can you do better to induce one worker to loaf and the other to work hard? How well do you do in this case?